
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 a sphere of radius \(3\) and eight smaller spheres each with radius \(1.5\), where the smaller spheres are each tangent to three sides of the box and the larger sphere is tangent to each of the smaller spheres, determine the value of \(h\).

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