に沿って details

にそって

in line with; along N (a plan, guideline, or physical line)

手順てじゅんに沿そってやったのに、なんかうまくいかないんだよね。

tejun ni sotte yatta noni, nanka umaku ikanai n da yo ne.

I did it following the steps, but somehow it's not working out, you know. casual

川かわに沿そって歩あるくと、古ふるい神社じんじゃが見みえてきます。

kawa ni sotte aruku to, furui jinja ga miete kimasu.

If you walk along the river, you'll come to see an old shrine. neutral

Examples

in line with; following — an action tracks a plan, guideline, or policy without deviating

手順てじゅんに沿そってやったのに、なんかうまくいかないんだよね。

tejun ni sotte yatta noni, nanka umaku ikanai n da yo ne.

I did it following the steps, but somehow it's not working out, you know. casual

この計画けいかくに沿そって、来月らいげつからプロジェクトを進すすめます。

kono keikaku ni sotte, raigetsu kara purojekuto o susumemasu.

Following this plan, we will move the project forward starting next month. neutral

各かく部署ぶしょは、本ほん方針ほうしんに沿そってご対応たいおうください。

kaku busho wa, hon houshin ni sotte go taiou kudasai.

Each department, please respond in accordance with this policy. formal

along; alongside — physically following a line such as a road, river, or coast

川かわに沿そって歩あるくと、古ふるい神社じんじゃが見みえてきます。

kawa ni sotte aruku to, furui jinja ga miete kimasu.

If you walk along the river, you'll come to see an old shrine. neutral

海岸かいがんに沿そって自転車じてんしゃで走はしったんだ、気持きもちよかったよ。

kaigan ni sotte jitensha de hashitta n da, kimochi yokatta yo.

I rode my bike along the coast — it felt great. casual

に沿い — て-drop for written and formal connecting clauses — 計画けいかくに沿そい、工事こうじを進すすめる; not used in conversation.
に沿った — modifies a following noun directly — マニュアルに沿そった作業さぎょう "work in line with the manual"; に沿って cannot sit in that slot.

に基づいて
Both require the noun to be a fixed reference the action stays faithful to, but に沿って's reference is a COURSE — a plan, guideline, or literal path the action tracks moment by moment without straying (計画に沿って進める) — while に基づいて's reference is a standard or piece of evidence a single judgment or product is built to be consistent with (証拠に基づいて判断する); に沿って reads as ongoing tracking along a line, に基づいて as one-time grounding in a source.
に応じて
に応じて demands a VARIABLE the outcome scales with — change the noun's value and the result changes too (収入に応じて税額が変わる), while に沿って demands a fixed guideline, plan, or path the action tracks without straying, and nothing in it varies proportionally (マニュアルに沿って作業する) — try に応じて on a rulebook that never changes and there is no scale left to respond to.