
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
If \((2x + 4)^{2n} = a_0 + a_1 x + a_2 x^2 + \cdots + a_{2n} x^{2n}\) \((n \in \mathbf{N}^{*})\), then the remainder when \(a_2 + a_4 + \cdots + a_{2n}\) is divided by 3 is \(\quad\)

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