
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
How many nonnegative integers can be written in the form \[b_8\cdot3^8 + b_7\cdot3^7 + b_6\cdot3^6 + b_5\cdot3^5 + b_4\cdot3^4 + b_3\cdot3^3 + b_2\cdot3^2 + b_1\cdot3^1 + b_0\cdot3^0,\] where \( b_i \in \{0, 1, 2\} \) for \( 0 \leq i \leq 8 \)?

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