
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 \( f(n) \) be the number of times you have to hit the \( \sqrt{ } \) key on a calculator to get a number less than 2 starting from \( n \). For instance, \( f(2) = 1 \), \( f(5) = 2 \). For how many \( 1 < m < 2008 \) is \( f(m) \) odd?

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