
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]


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The lateral faces of a pentagonal pyramid \( S A B C D E \) are acute-angled triangles. We will call a lateral edge of the pyramid good if it is equal to the height of the opposite lateral face, drawn from the apex of the pyramid. For example, edge \( S A \) is good if it is equal to the height of triangle \( S C D \), drawn from vertex \( S \). What is the maximum number of good edges that the pyramid can have?

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