
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
In the plane rectangular coordinate system $(xOy)$, given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with $|\overrightarrow{a}| = |\overrightarrow{b}| = 1$ and $\overrightarrow{a} \cdot \overrightarrow{b} = 0$, express the inequality concerning the parameters $r$ and $R$ for which curve $C = \{P | \overrightarrow{OP} = \overrightarrow{a}\cos\theta + \overrightarrow{b}\sin\theta, 0 \leq \theta \leq 2\pi\}$ intersects with region $\Omega = \{P | 0 < r \leq |\overrightarrow{PQ}| \leq R, r < R\}$ in two separate curves.

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