
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
Given that in triangle ABC with ∠C = 120°, M is the midpoint of AB, D is a point on BC such that BD:DC = 3:2, and E is the midpoint of AC, determine the area of triangle BME if the area of triangle ABC is 36 square units.

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