
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
What is the maximum number of coins can be arranged in cells of the table  $n \times n$  (each cell is not more of the one coin) so that any coin was not simultaneously below and to the right than any other?

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