
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
Alice has an equilateral triangle \(ABC\) with an area of 1. Point \(D\) is on \(BC\) such that \(BD = DC\), point \(E\) is on \(CA\) such that \(CE = 2EA\), and point \(F\) is on \(AB\) such that \(2AF = FB\). Line segments \(AD\), \(BE\), and \(CF\) intersect at a single point \(M\). What is the area of triangle \(EMC\)?

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