
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
Consider the function $k(x)$ defined by the equation
\[(x^{2^{2008}-2}-1)k(x) = (x+2)(x^2+2)(x^4+2)\cdots (x^{2^{2007}}+2) - 1.\]
Find $k(3)$.

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