
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 geometric sequence $\{a_{n}\}$ where $a_{2}=1$ and $a_{9}=9$. Find the value of $f'\left(0\right)$ for the function $f\left(x\right)=x(x-a_{1})(x-a_{2})\ldots (x-a_{10})$.

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