
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 equilateral  $\triangle ABC$  let points  $D$  and  $E$  trisect  $\overline{BC}$ .  Then  $\sin \left( \angle DAE \right)$  can be expressed in the form  $\tfrac{a\sqrt{b}}{c}$ , where  $a$  and  $c$  are relatively prime positive integers, and  $b$  is an integer that is not divisible by the square of any prime.  Find  $a+b+c$ .

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