
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 rectangular floor, twice as long as it is wide, is covered with congruent square tiles. If the total number of tiles that lie on both diagonals is 39, determine the total number of tiles that cover the floor.

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