
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
Consider a $6\times 6\times h$ rectangular box containing a larger sphere of radius $3$ and four smaller spheres, each with radius $2$. The smaller spheres are placed at each corner of the bottom square face of the box and are tangent to two adjacent sides of the box. The larger sphere is tangent to all four smaller spheres. Determine the height $h$ of the box required to accommodate this configuration.
A) $5$
B) $5 + \sqrt{21}$
C) $5 + \sqrt{23}$
D) $5 + \sqrt{25}$
E) $5 + 2\sqrt{23}$

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