
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
Calculate the value of \( n \) for which the sum $$2 + 33 + 444 + 5555 + 66666 + 777777 + 8888888 + 99999999$$ is congruent to \( n \) modulo 9, where \( 0 \leq n < 9 \). Additionally, find out if \( n \) is even or odd.

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