
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 a function $f(x)$ that satisfies: ① The graph of $f(x)$ passes through the point $(8, \frac{3}{2})$; ② $f(x)$ is an even function; ③ For any non-zero real numbers $x_1, x_2$, if $f(x_1) = f(x_2)$, then $f(\frac{x_1}{x_2}) = f(x_2)$. Please write down a function $f(x) = \_\_\_\_\_\_$ that satisfies the above conditions.

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