
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
It is known that the graph of the function $f(x)$ is symmetric to the graph of the function $g(x) = a^x$ with respect to the line $y = x$.
(1) Find the analytical expression of the function $f(x)$;
(2) When $a > 1$, if $f(x) < f(2)$, try to determine the range of the real number $x$.

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