
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
If  $-3 \le x < \frac{3}{2}$  and  $x \ne 1$ , define  $C(x) = \frac{x^3}{1 - x}$ .  The real root of the cubic  $2x^3 + 3x - 7$  is of the form  $p C^{-1}(q)$ , where  $p$  and  $q$  are rational numbers.  What is the ordered pair  $(p, q)$ ?

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