
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 the pole of the polar coordinate system coincides with the origin of the rectangular coordinate system, and the polar axis coincides with the positive semi-axis of the $x$-axis of the rectangular coordinate system. The polar equation of the curve $C$ is $7ρ^{2}-ρ^{2}\cos 2θ-24=0$.

1. Find the rectangular equation of the curve $C$.
2. If a point $(x, y)$ is on the curve $C$, find the range of values for $x - 2y$.

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