
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 lengths of the hypotenuse and one of the legs of a right triangle are 13 meters and 5 meters, respectively. Inside this triangle, there is a smaller right triangle formed by halving the longest leg of the original triangle (that is not the hypotenuse). What is the total shaded area, i.e., the area of the original triangle minus the area of the smaller triangle?

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