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

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