
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 expressed as \[b_6\cdot4^6+b_5\cdot4^5+b_4\cdot4^4+b_3\cdot4^3+b_2\cdot4^2+b_1\cdot4^1+b_0\cdot4^0,\] where $b_i \in \{-1,0,1\}$ for $0 \leq i \leq 6$?

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