
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
Let \([x]\) denote the greatest integer less than or equal to the real number \(x\). Define
\[ A = \left[\frac{19}{20}\right] + \left[\frac{19^2}{20}\right] + \cdots + \left[\frac{19^{2020}}{20}\right]. \]

Find the remainder when \(A\) is divided by 11.

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