
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
Find the largest \( k \) such that \( 1991^{k} \) divides \( A = 1990^{1991^{1992}} + 1991^{1990^{1992}} + 1992^{1991^{1990}} \).

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