
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
Triangle \( \triangle ABC \) has area 1. Points \( E \) and \( F \) are on \( AB \) and \( AC \) respectively such that \( EF \parallel BC \). If \( \triangle AEF \) and \( \triangle EBC \) have equal areas, find the area of \( \triangle EFC \).

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