
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 $ABC$, a median $AM$ is drawn, with point $O$ being the center of the circumcircle, and point $Q$ being the center of the incircle. Segments $AM$ and $OQ$ intersect at point $S$, and it is given that $2 \frac{OS}{MS} = 3 \sqrt{3} \frac{QS}{AS}$. Find the sum of the sines of the angles $ABC$ and $ACB$, given that $\angle BAC = \frac{\pi}{3}$. Round the answer to the nearest hundredth if necessary.

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