
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 odd function f(x) = $$\frac{a \cdot 2^x - 1}{2^x + 1}$$ with a domain of $[-a - 2, b]$,

1. Find the values of the real numbers $a$ and $b$.
2. Determine the monotonicity of the function $f(x)$ and provide a proof using the definition.
3. If the real number $m$ satisfies $f(m - 1) < f(1 - 2m)$, find the range of $m$.

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