
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 function defined on \( \mathbb{R} \) with a period of 2, when \( x \in [-1,1) \), \( f(x)=\begin{cases} -4x^{2}+2 & -1\leqslant x < 0 \\\\ x & 0\leqslant x < 1 \end{cases} \). Evaluate \( f\left(\frac{3}{2}\right) \).

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