
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 $\theta$ is a root of $g(x)=x^{4}-7x^{2}+1$, and $h(x)$ is a quadratic function with rational coefficients such that $h\left(\theta^{2}-1\right)=0$, find the roots of $h(x)=0$.

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