
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 sphere with radius $\sqrt{5}$ centered at point $O$ touches all sides of triangle $ABC$. The point of tangency $N$ divides side $AB$ in half. The point of tangency $M$ divides side $AC$ such that $AM = \frac{1}{2} MC$. Find the volume of the pyramid $OABC$, given that $AN = NB = 1$.

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