
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
There exist $s$ unique nonnegative integers $m_1 > m_2 > \cdots > m_s$ and $s$ unique integers $b_k$ ($1\le k\le s$) where each $b_k$ is either $2$, $1$, or $-1$ such that
\[b_12^{m_1} + b_22^{m_2} + \cdots + b_s2^{m_s} = 4030.\]
Find $m_1 + m_2 + \cdots + m_s$.

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