
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 $f(x)$ be a periodic function defined on $(-\infty, +\infty)$ with a period of $2$, and $f(x)$ be an even function. On the interval $[2,3]$, $f(x)=-2(x-3)^{2}+4$. Find $f(x)$ when $x \in [0,2]$.

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