
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
A circle centered at $O$ has radius 3 and contains the point $A$. Segment $AB$ is tangent to the circle at $A$, and $\angle AOB = 120^\circ$. If point $D$ lies on segment $\overline{OA}$ and point $C$ lies on the circle such that $\angle BOC$ is a right angle, express $OD$ in terms of $s$ and $c$, where \( s = \sin(120^\circ) \) and \( c = \cos(120^\circ) \).

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