
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
The function \( f \) is defined on the set of natural numbers and satisfies the following conditions:
(1) \( f(1)=1 \);
(2) \( f(2n)=f(n) \), \( f(2n+1)=f(2n)+1 \) for \( n \geq 1 \).

Find the maximum value \( u \) of \( f(n) \) when \( 1 \leq n \leq 1989 \) and determine how many values \( n \) (within the same range) satisfy \( f(n)=u \).

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