
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
A function \( f \) is defined on the positive integers by: \( f(1) = 1 \); \( f(3) = 3 \); \( f(2n) = f(n) \), \( f(4n + 1) = 2f(2n + 1) - f(n) \), and \( f(4n + 3) = 3f(2n + 1) - 2f(n) \) for all positive integers \( n \). Determine the number of positive integers \( n \) less than or equal to 1988 for which \( f(n) = n \).

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