
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 $\triangle RED$, $\measuredangle DRE=60^\circ$ and $\measuredangle RED=60^\circ$. $RD=2$. Let $M$ be the midpoint of segment $\overline{RD}$. Point $C$ lies on side $\overline{ED}$ such that $\overline{RC}\perp\overline{ED}$. Extend segment $\overline{DE}$ through $E$ to point $A$ such that $EA = 3AD$. Find the length of $EA$.

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