
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
Let \( s \) be the positive real solution to the equation \( x^3 - \frac{3}{4}x + 2 = 0 \). Find the exact numerical value of
\[ s^2 + 2s^4 + 3s^6 + 4s^8 + \dotsb. \]

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