
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 $f(x) = -x^2 - x^4 - x^6$, and $x_1, x_2, x_3 \in \mathbb{R}$ with $x_1 + x_2 < 0$, $x_2 + x_3 < 0$, $x_3 + x_1 < 0$, calculate the value of $f'(x_1) + f'(x_2) + f'(x_3)$.

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