
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 function $f(x)$ be an even function, and for all $x \in \mathbb{R}$, we have $f\left(x- \frac{3}{2}\right) =f\left(x+ \frac{1}{2}\right)$. When $x \in [2,3]$, $f(x)=x$. Determine the expression for $f(x)$ when $x \in [-2,0]$.

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