
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
A quadrilateral and a pentagon are given on the plane (both may be non-convex), such that no vertex of one lies on the side of the other. What is the maximum possible number of points of intersection of their sides?

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