
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 system of equations $$\begin{cases} a^{2}\sin\theta + a\cos\theta - 1 = 0 \\ b^{2}\sin\theta + b\cos\theta - 1 = 0 \end{cases}$$ where $a \neq b$, find the distance from the origin $(0, 0)$ to the line passing through the points $(a, a^{2})$ and $(b, b^{2})$.

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