
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
The side lengths of a triangle are integers. It is known that the altitude drawn to one of the sides divides it into integer segments, the difference of which is 7. For what minimum value of the length of this side, the altitude drawn to it is also an integer?

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