
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
The algae in a small lake in Central Park grow so quickly that the surface area covered by the algae doubles every day. On the $20^{th}$ day of the month, the lake was completely covered with algae. Determine on which day of that month was $90\%$ of the lake algae-free.

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