
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 the function $f(x)$ is symmetric about the line $x=-2$ and has a period of $2$, and when $x \in [-3, -2]$, $f(x) = (x + 2)^2$, find $f(\frac{5}{2})$.

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