
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
Consider two convex polygons $Q_1$ and $Q_2$ drawn in the same plane where polygon $Q_1$ is nested inside polygon $Q_2$. $Q_1$ has $m$ sides and $Q_2$ has $2m$ sides, where $m \geq 3$. They don't share any line segment, and both polygons are convex. What is the maximum number of intersections between $Q_1$ and $Q_2$?
A) $m^2$
B) $m$
C) $2m^2$
D) $3m$
E) $4m^2$

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