
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
Let \( f: \mathbb{N}^{*} \rightarrow \mathbb{N}^{*} \) be a function that satisfies the following conditions:

1. \( f(1)=1 \)
2. \( f(2n)=f(n) \)
3. \( f(2n+1)=f(n)+1 \)

What is the greatest value of \( f(n) \) for \( 1 \leqslant n \leqslant 2018 \) ?

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