
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 $x \in [-1, 1)$,
$$
f(x) =
\begin{cases}
-4x^2 + 2, & -1 \leq x < 0\\
x, & 0 \leq x < 1.
\end{cases}
$$
Find $f\left( \frac{5}{2} \right)$ = $\_\_\_\_\_\_$

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