
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
In the non-decreasing sequence of even integers \(\{a_1,a_2,a_3,\ldots\}=\{2,4,4,6,6,6,8,8,8,8,\ldots\}\) each even positive integer \(k\) appears \(k/2\) times, determine the value of \(b+c+d\).

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