
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 an even function defined on $\mathbb{R}$ with a period of $2$. When $x \in [-1, 0)$, $f(x) = 4^x + 1$. Find $f(\frac{5}{2})$ = \_\_\_\_\_\_.

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