
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 convex polyhedron has faces that are either pentagons or hexagons, and exactly three edges meet at each vertex. How many pentagonal faces does the polyhedron have? Provide an example of such a polyhedron.

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