
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
An isosceles triangle with a median to the base measuring 15 units has a base length of 36 units. If the vertex angle opposite the base is 60 degrees, what is the length of each of the equal sides?

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