
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
Define a function on the positive integers recursively by  $f(1) = 2$ ,  $f(n) = f(n-1) + 1$  if  $n$  is even, and  $f(n) = f(n-2) + 2$  if  $n$  is odd and greater than  $1$ . What is  $f(2017)$ ?

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