
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
There are 2021 balls in a crate, numbered from 1 to 2021. Erica calculates the digit sum for each ball. For example, the digit sum of 2021 is 5, since \(2+0+2+1=5\). Balls with equal digit sums have the same color and balls with different digit sums have different colors. How many different colors of balls are there in the crate?

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