
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
Given a $6 \times 6 \times h$ rectangular box contains two spheres each of radius $3$ and eight smaller spheres of radius $1.5$, and each of the smaller spheres is tangent to three faces of the box, each larger sphere is tangent to four of the smaller spheres, and the two larger spheres are also tangent to each other, find the value of $h$.

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