
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 block, which has dimensions $n$ by 11 by 10, is made up of a number of unit cubes and one 2 by 1 by 1 block. Given that there are exactly 2362 positions in which the 2 by 1 by 1 block can be placed, determine the value of $n$.

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