
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 area of triangle $ABC$ is 1. Let $A_1, B_1, C_1$ be the midpoints of the sides $BC, CA, AB$ respectively. Points $K, L, M$ are taken on the segments $AB_1, CA_1, BC_1$ respectively. What is the minimum area of the common part of triangles $KLM$ and $A_1B_1C_1$?

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