
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 defined on R, f(x) = 4^x - m * 2^(x+1) + m^2 - 3.
(1) Solve the inequality f(x) > 1 when m = 1.
(2) Find the possible values of the real number m such that there exists an x0 in R, and f(-x0) = -f(x0).

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