
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
In right triangle $ABC$, with $AB$ as the hypotenuse, points $E$ and $F$ divide sides $\overline{AC}$ and $\overline{AB}$ in the ratios $1:3$ and $2:1$, respectively. The area of $\triangle ABC$ is 50 square units. What is the area of $\triangle CEF$?

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