
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 $6\times 6\times h$ rectangular box contains a sphere of radius $3$ and eight smaller spheres of radius $2$. The smaller spheres are each tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres, not at the center but offset along one dimension. What is $h$?
A) $\sqrt{49}$
B) $\sqrt{65}$
C) $5 + \sqrt{65}$
D) $2 + \sqrt{65}$

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