
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 that \( f(x) \) is an odd function defined on \( \mathbf{R} \), and for any \( x \in \mathbf{R} \), the following holds:
$$
f(2+x) + f(2-x) = 0.
$$

When \( x \in [-1, 0) \), it is given that
$$
f(x) = \log_{2}(1-x).
$$

Find \( f(1) + f(2) + \cdots + f(2021) \).

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