
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 large square dance floor is fully covered with congruent square tiles. Tiles laid along the two intersecting diagonals of the square floor are marked in blue. All other tiles remain uncolored. Given that there are 225 blue colored tiles in total, determine the overall number of tiles on the floor.
A) 625
B) 10609
C) 12769
D) 14400
E) 16129

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