
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 $ABC$ is an equilateral triangle with side length $AB = 2$. Points $E$ and $G$ are on line $\overline{AC}$, and points $D$ and $F$ are on line $\overline{AB}$ such that both lines $\overline{DE}$ and $\overline{FG}$ are parallel to $\overline{BC}$. Furthermore, triangle $ADE$ and trapezoids $DFGE$ and $FBCG$ all have the same perimeter. How much is $DE + FG$?
A) 4
B) 5
C) 6
D) 7

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