
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 $\triangle ABC$, $AB = AC = x$ and $BC = y$. Points $D, E, F$ are on sides $\overline{AB}, \overline{BC}, \overline{AC}$ respectively, such that $\overline{DE}$ and $\overline{EF}$ are parallel to $\overline{AC}$ and $\overline{AB}$ respectively, with $DE = \frac{1}{3}AC$ and $EF = \frac{1}{3}AB$. Determine the perimeter of parallelogram $ADEF$, given that $x = 33$ and $y = 31$.

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