
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
If the odd function \( f(x) \) is defined on \( (-\infty, 0) \cup (0, +\infty) \) and is increasing on \( (0, +\infty) \), \( f(1) = 0 \). Also, there is a function \( g(\theta) = \sin^2 \theta + m \cos \theta - 2m \), where \( \theta \in \left[0, \frac{\pi}{2}\right] \). Given the set \( M = \{m \mid g(\theta) < 0\} \) and the set \( N = \{m \mid f[g(\theta)] < 0\} \), find the set \( M \cap N \).

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