
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 $f(x)= \frac {1}{3}x^{3}+x$, $x\in\mathbb{R}$, if there exists at least one real number $x$ such that $f(a-x)+f(ax^{2}-1) < 0$ holds, the range of $a$ is \_\_\_\_\_\_.

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