
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
(For liberal arts) Define a new operation "$\ast$" for any positive integer $n$ that satisfies the following two conditions: (1) $1 \ast 1 = 1$, (2) $(n+1) \ast 1 = 2 + (n \ast 1)$. Then, find the value of $2006 \ast 1$.

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