
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 a right square pyramid $O-ABCD$, $\angle AOB=30^{\circ}$, the dihedral angle between plane $OAB$ and plane $OBC$ is $\theta$, and $\cos \theta = a \sqrt{b} - c$, where $a, b, c \in \mathbf{N}$, and $b$ is not divisible by the square of any prime number. Find $a+b+c=$ _______.

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