
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 $f(x)$ defined on the interval $(0,+\infty)$ satisfies $f(x\_1\cdot x\_2)=f(x\_1)+f(x\_2)$, and $f(x) > 0$ when $x > 1$.

(1) Find the value of $f(1)$;

(2) If $f(\frac{1}{5})=-1$, find the maximum and minimum values of $f(x)$ on $[\frac{1}{25},125]$.

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