
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 the function $f(x)=ax^{2}+bx+c(a\\neq 0)$, its graph intersects with line $l$ at two points $A(t,t^{3}-t)$, $B(2t^{2}+3t,t^{3}+t^{2})$, where $t\\neq 0$ and $t\\neq -1$. Find the value of $f{{'}}(t^{2}+2t)$.

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