
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 $a > 1$, the graph of function $f(x)$ is symmetric to the graph of the function $y = 4 - a^{|x-2|} - 2 \cdot a^{x-2}$ with respect to point $A(1, 2)$.
(1) Find the analytical expression of function $f(x)$;
(2) If the equation $f(x) = m$ has two different positive solutions for $x$, find the range of values for the real number $m$.

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