
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-shaped floor is covered with congruent square tiles. Along with the two diagonals of the square and a horizontal line through its center that includes additional tiles, the total number of tiles along the two diagonals and this central line is 55. Determine the number of tiles that cover the entire floor.

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