
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 the function $f(x)=\log_{a}x (a > 0, a \neq 1)$, and $f(3)-f(2)=1$.

(1) Find the range of the real number $m$ that satisfies $f(3m-2) < f(2m+5)$;

(2) Find the value of $x$ that satisfies the equation $f(x-\frac{2}{x})=\log_{\frac{3}{2}}\frac{7}{2}$.

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