
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 two parallel lines $l_1$ and $l_2$, point $A$ is a fixed point between $l_1$ and $l_2$. The distances from point $A$ to $l_1$ and $l_2$ are 3 and 2, respectively. Point $B$ is a moving point on $l_2$. Construct $AC \perp AB$, and $AC$ intersects $l_1$ at point $C$. Find the minimum value of the area of $\triangle ABC$.

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