
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
The side $AB$ of triangle $ABC$ is extended beyond vertex $B$ and a point $A_1$ is chosen on the ray $AB$ such that point $B$ is the midpoint of segment $AA_1$. The side $BC$ is extended beyond vertex $C$ and a point $B_1$ is marked on the extension such that $C$ is the midpoint of $BB_1$. Similarly, the side $CA$ is extended beyond vertex $A$ and a point $C_1$ is marked on the extension such that $A$ is the midpoint of $CC_1$. Find the area of triangle $A_1B_1C_1$ if the area of triangle $ABC$ is 1.

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