
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 an operation "$\ast$" for positive integers that satisfies the following properties:
(1) $2 \ast 2006 = 1$; (2) $(2n+2) \ast 2006 = 3 \cdot [(2n) \ast 2006]$, then the value of $2008 \ast 2006$ is.

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