
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 defined on $\mathbb{R}$ and has a period of $4$ as an even function. When $x \in [2,4]$, $f(x)=|\log_{4}(x-\frac{3}{2})|$, then the value of $f(\frac{1}{2})$ is.

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