
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  $\mathbb{N}_0$  and  $\mathbb{Z}$  be the set of all non-negative integers and the set of all integers, respectively. Let  $f:\mathbb{N}_0\rightarrow\mathbb{Z}$  be a function defined as
\[f(n)=-f\left(\left\lfloor\frac{n}{3}\right\rfloor \right)-3\left\{\frac{n}{3}\right\} \]
where  $\lfloor x \rfloor$  is the greatest integer smaller than or equal to  $x$  and  $\{ x\}=x-\lfloor x \rfloor$ . Find the smallest integer  $n$  such that  $f(n)=2010$ .

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