
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
Edit the calculation program: $1 \& 1 = 2$, $m \& n = k$, $m \& (n+1) = k+3$ ($m, n, k \in \mathbb{N}^*$), then calculate the output of $1 \& 2010$.

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