
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 that \( f(x) \) is an odd function defined on \( R \) and is monotonically increasing for \( x<0 \) with \( f(-1) = 0 \), let \( \varphi(x) = \sin^2 x + m \cdot \cos x - 2m \). Define the set \( M = \{ m \mid \forall x \in [0, \frac{\pi}{2}], \varphi(x) < 0 \} \) and the set \( N = \{ m \mid \forall x \in [0, \frac{\pi}{2}], f(\varphi(x)) < 0 \} \). Find \( M \cap N \).

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