
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 constant such that $0 < \theta < \frac{\pi}{2}$ and $x + \dfrac{1}{x} = 2\sin{\theta}$, for each positive integer $n$, calculate $x^n + \dfrac{1}{x^n}$.

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