
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 function \( f(x) \) defined on \( \mathbf{R} \) such that \( f(x) \) is an odd function and an increasing function on \( [0, +\infty) \), for any \( x \in \mathbf{R} \), find a real number \( m \) such that \( f(\cos 2 \theta - 3) + f(4m - 2m \cos \theta) > 0 \) always holds.

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