
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
Given \(a_{1}, a_{2}, \cdots, a_{2m+1}\) are \(2m+1\) real numbers, with each pair of adjacent numbers \(a_{n}, a_{n+1}\) being the roots of the equation \(x^2 + 4nx + b_n = 0\). Find the value of \(\sum_{n=1}^{2m} b_n\) when \(a_{1} = 0\).



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