
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  $f : N \to N$  be a strictly increasing function such that  $f(f(n))= 3n$ , for all  $n \in N$ . Find  $f(2010)$ . 

Note:  $N = \{0,1,2,...\}$ 

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