
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
Suppose $\triangle ABC$ is defined by vertices $A = (0,2)$, $B = (0,0)$, and $C = (10,0)$. Find the x-coordinate $a$ of a vertical line $x = a$ that divides the triangle into two regions of equal area.

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