
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
Let $(1+x+x^3)^n = b_0 + b_1x + b_2x^2 + \cdots + b_{3n}x^{3n}$ be an identity in $x$. For the sum $t = b_0 + b_3 + b_6 + \cdots$, determine the value of $t$.
A) $3^n$
B) $2^n$
C) $2^n + 1$
D) $3^n - 1$

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