
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
Let cone $O-ABC$ have a circular base where $O$ is the vertex and $ABC$ form a triangle within the base circle. The angles $\angle OAB = \angle OBC = \angle OCA = 90^\circ$. Define $a = \sin \angle AOC$ and $b = \sin \angle BOC$. Express $\cos \angle BAC$ in terms of $a$ and $b$.

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