
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 right triangular prism has base edges of lengths $a = 5$ m and $b = 12$ m, and height $c = 13$ m. The triangular base is a right triangle. A rectangular face of the prism has dimensions $5$ m, $12$ m, and the third dimension $h$. If the body diagonal of the prism is $15$ m, what is the measure of $h$?

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