
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 castle has the shape of a heptagon, with a watchtower at each vertex. Each of the seven walls of the castle is guarded by the watchmen in the towers located at the ends of that wall. What is the minimum number of watchmen that need to be placed in the towers so that each wall is guarded by at least seven watchmen?

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