
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
On the extensions of the sides of triangle $ABC$, points $A_{1}$, $B_{1}$, and $C_{1}$ are taken such that $\overrightarrow{A B_{1}} = 2 \overrightarrow{A B}$, $\overrightarrow{B C_{1}} = 2 \overrightarrow{B C}$, and $\overrightarrow{C A_{1}} = 2 \overrightarrow{A C}$. Find the area of triangle $A_{1} B_{1} C_{1}$, given that the area of triangle $ABC$ is $S$.

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