
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 $1$. Each smaller sphere is tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres. Determine the height $h$ of the box.
A) 6
B) 8
C) 10
D) 12

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