
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
Let $f(x)$ ($x\in\mathbb{R}$) be a periodic function with a period of 4 and $f(-x) + f(x) = 0$. Given that $f(x) = (x-1)^2$ for $x\in[0,2]$, find the value of $f(3)$.

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