
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 a given natural number \( k \), define \( f_1(k) \) as the square of the sum of the digits of \( k \), and let \( f_{n+1}(k) = f_1(f_n(k)) \). Find the value of \( f_{1991}(2^{1990}) \).

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