
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
(1) Given $f(3^{x})=x \lg 9$, find the value of $f(2)+f(5)$;
(2) If $3^{a}=5^{b}=A(ab\neq 0)$, and $\frac{1}{a}+\frac{1}{b}=2$, find the value of $A$.

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