
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
Consider two isosceles triangles placed back-to-back with their bases along the x-axis. They share a common vertex at point $(10, 0)$. Each triangle has a base of $12$ units and a height of $10$ units. A line is drawn from the vertex opposite the base of the left triangle to the vertex opposite the base of the right triangle. Calculate the area of the shaded region formed between this line and the bases of the triangles.

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