
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 triangle $ABC$, $A$, $B$, $C$ are its three internal angles, and the lengths of the sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$, with $c=2$ and $C= \dfrac{\pi}{3}$. Let $m=(\sin C+\sin (B-A),4)$ and $n=(\sin 2A,1)$. If $m$ and $n$ are collinear, then the area of $\triangle ABC$ is ______.

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