
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 number of spheres with radius  $ 1$  are being placed in the form of a square pyramid. First, there is a layer in the form of a square with  $ n^2$  spheres. On top of that layer comes the next layer with  $ (n\minus{}1)^2$  spheres, and so on. The top layer consists of only one sphere. Compute the height of the pyramid.

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