
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 two convex polygons $A_1$ and $A_2$ in the same plane, where $A_1$ has $m$ sides and $A_2$ has $m+2$ sides, and any side of $A_1$ intersects with any side of $A_2$ without overlapping, calculate the maximum number of points at which $A_1$ and $A_2$ can intersect.

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