
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
Consider a large square floor divided into smaller square sections. The floor is tiled entirely with square tiles, and a distinct decoration involves marking some tiles black. Specifically, tiles along the north-east to south-west diagonal are black. Moreover, rows and columns are symmetric around the center of the square: the number of black tiles in each row increases by one as we move from the outermost row toward the middle row, where it reaches its maximum. Given that there are 49 black tiles on the middle row, determine the total number of tiles on the floor.
A) 3844
B) 9409
C) 9801
D) 6724
E) 10201

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