
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 triangle with sides 13, 14, and 15 is divided into three equal parts by lines perpendicular to the longest side. Find the distances to these lines from the nearest vertices of the triangle, which are located on the longest side.

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