
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 large square is divided into nine smaller squares of equal area. The left column and the top row squares are then filled. This pattern of shading the left column and the top row continues indefinitely as each non-shaded square gets further divided into nine smaller squares of equal area. Determine what fractional part of the entire square is shaded.

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