
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 set of natural numbers and satisfies the following conditions:
(1) \( f(1) = 1 \);
(2) \( f(2n) = f(n) \) and \( f(2n + 1) = f(2n) + 1 \) for \( n \geq 1 \).

Determine the maximum value \( u \) of \( f(n) \) when \( 1 \leq n \leq 1989 \). Additionally, find out how many values of \( n \) in the range \( 1 \leq n \leq 1989 \) satisfy \( f(n) = n \).

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