
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
(The full score of this question is 14 points) It is known that the odd function $f(x)$ is defined on $(-\infty,0)\cup(0,+\infty)$ and is increasing on $(0,+\infty)$. Given $f(1) = 0$, and the function $g(q) = \sin 2q + m \cos q - 2m$, if the set $M = \{m | g(q) < 0\}$, and the set $N = \{m | f[g(q)] < 0\}$, find $M \cap N$.

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