
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 \( [x] \) denote the greatest integer not exceeding \( x \), e.g., \( [\pi]=3 \), \( [5.31]=5 \), and \( [2010]=2010 \). Given \( f(0)=0 \) and \( f(n)=f\left(\left[\frac{n}{2}\right]\right)+n-2\left[\frac{n}{2}\right] \) for any positive integer \( n \). If \( m \) is a positive integer not exceeding 2010, find the greatest possible value of \( f(m) \).

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