
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
The function  $f : \mathbb{R}\to\mathbb{R}$  satisfies  $f(x^2)f^{\prime\prime}(x)=f^\prime (x)f^\prime (x^2)$  for all real  $x$ .  Given that  $f(1)=1$  and  $f^{\prime\prime\prime}(1)=8$ , determine  $f^\prime (1)+f^{\prime\prime}(1)$ .

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