
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
Points \( A_1 \), \( B_1 \), and \( C_1 \) are located on the sides \( BC \), \( AC \), and \( AB \) of triangle \( ABC \) respectively, such that \( BA_1 : A_1C = CB_1 : B_1A = AC_1 : C_1B = 1 : 3 \). Find the area of the triangle formed by the intersections of the lines \( AA_1 \), \( BB_1 \), and \( CC_1 \), given that the area of triangle \( ABC \) is 1.

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