
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
For any positive integer \( k \), let \( f_1(k) \) be defined as the square of the sum of the digits of \( k \). For \( n \geq 2 \), let \( f_n(k) = f_1(f_{n-1}(k)) \). Find \( f_{1988}(11) \).

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