
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 $\triangle BAC$, $\angle BAC=60^\circ$, $AB=8$, and $AC=5$. Points $D$ and $E$ lie on $\overline{AB}$ and $\overline{AC}$ respectively such that $AD = 3$ (point $D$ is between $A$ and $B$) and $AE = 2$ (point $E$ is between $A$ and $C$). Determine the minimum possible value of $BE+DE+CD$.
A) $\sqrt{52} + \sqrt{24} + 2$
B) $\sqrt{52} + 8$
C) $\sqrt{52} + \sqrt{34} + 2$
D) $\sqrt{86} + 2$
E) 10

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