
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
In the plane where $\triangle ABC$ is located, there is a point $P$ that satisfies $\overset{⇀}{PA} + \overset{⇀}{PC} = m \overset{⇀}{AB}$ ($m > 0$, $m$ is a constant). If the area of $\triangle ABP$ is $6$, what is the area of $\triangle ABC$?

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