
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
Given an isosceles triangle $\triangle ABC$ with vertices at $A = (0, 4)$, $B = (0, 0)$, and $C = (4, 4)$. Find the equation of the vertical line $x = a$ that divides $\triangle ABC$ into two regions of equal area.
A) $x = 1$
B) $x = 2$
C) $x = 3$
D) $x = 4$

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