
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
Determine the number of nonnegative integers that can be written in the form \[
b_7\cdot3^7 + b_6\cdot3^6 + b_5\cdot3^5 + b_4\cdot3^4 + b_3\cdot3^3 + b_2\cdot3^2 + b_1\cdot3^1 + b_0\cdot3^0,
\] where \(b_i \in \{0, 1, 2\}\) for \(0 \leq i \leq 7\).

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