
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 that for any $x\in R$, it always holds that $f(-x)=-f(x)$, $g(-x)=g(x)$, and when $x > 0$, $f′(x) > 0$, $g′(x) > 0$, determine the behavior of $f′(x)$ and $g′(x)$ when $x < 0$.

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