
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
Little Tiger places chess pieces on the grid points of a 19 × 19 Go board, forming a solid rectangular dot matrix. Then, by adding 45 more chess pieces, he transforms it into a larger solid rectangular dot matrix with one side unchanged. What is the maximum number of chess pieces that Little Tiger originally used?

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