
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
Given a square floor tiled with congruent square tiles, the tiles on the two diagonals of the floor are black, while the rest of the tiles are white, find the total number of tiles if there are 101 black tiles.

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