
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 $t$ be the positive real solution to $x^3 + \frac{3}{7}x - 1 = 0.$ Find the exact numerical value of
\[
t^3 + 2t^6 + 3t^9 + 4t^{12} + \dotsb.
\]

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