
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
If for any \( x \in \left( -\frac{1}{2}, 1 \right) \), the following equation holds:
\[
\frac{x}{1+x-2x^{2}} = a_{0} + a_{1} x + a_{2} x^{2} + \cdots + a_{n} x^{n} + \cdots
\]
then the value of \( a_{3} + a_{4} \) is _______

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