
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 $5 \times 5 \times h$ rectangular box contains a sphere of radius $2.5$ and eight smaller spheres of radius $1$. Each of the smaller spheres is tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres. What is $h$?
A) \(3 + 2\sqrt{8.75}\)
B) \(2 + 2\sqrt{7.75}\)
C) \(4 + 2\sqrt{8}\)
D) \(3 + 2\sqrt{7}\)

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