
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 square floor is fully covered with square tiles of the same size. Black tiles are placed along the two diagonals, and white tiles are used to cover the other areas. If there are a total of 101 black tiles, calculate the total number of tiles used to cover the entire floor.

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