
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
Consider a $7\times7$ chessboard, which has its lines dividing the board into smaller rectangles and squares. Calculate the number of rectangles and squares formed by these lines. Then find the ratio of the number of squares to rectangles, simplified to its lowest terms, and determine the sum of the numerator and denominator of this fraction.

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