
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the sequence $\left\{a_{n}\right\}$ such that:
$$
a_{1}=-2,
$$

and $S_{n}=\frac{3}{2} a_{n}+n$ (where $S_{n}$ is the sum of the first $n$ terms of the sequence $\left\{a_{n}\right\}$). Let $f(x)$ be an odd function defined on $\mathbf{R}$, which satisfies:
$$
f(2-x)=f(x).
$$

Find $f\left(a_{2021}\right)=$ $\qquad$

Present the answer in LaTex format: \boxed{Your answer}
user