
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 $f(x) = \frac{2^x - 1}{2^x + 1}$ ($x \in \mathbb{R}$).
1. Determine the parity of the function $f(x)$.
2. Use the definition to determine the monotonicity of the function $f(x)$.
3. Solve the inequality $f(1-m) + f(1-m^2) < 0$.

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