
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 soccer ball is sewn from 32 patches: white hexagons and black pentagons. Each black patch borders only white ones, and each white one borders three black and three white ones. How many white patches are there?

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