
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 room is covered with congruent square tiles. The total number of tiles along its two diagonals is 57. Additionally, count the total number of triangles formed by these diagonals and any two adjacent sides of the square room.

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