
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
Given the pattern of the number of shaded squares follows the sequence of squared numbers (1, 4, 9, 16, 25, 36, 49, 64,...) for the first eight squares, calculate the fraction of the eighth square that would be shaded.

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