
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
Let \( r \) be some real constant, and \( P(x) \) a polynomial which has remainder 2 when divided by \( x-r \), and remainder \(-2 x^{2}-3 x+4\) when divided by \(\left(2 x^{2}+7 x-4\right)(x-r)\). Find all values of \( r \).

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