
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
Three altitudes of a tetrahedron are three, four, and four times longer than the radius of its inscribed sphere, respectively. By how many times is the fourth altitude longer than the radius of the inscribed sphere?

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