
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
For which values of the parameters \( a \) and \( b \) will the equation 

\[
\frac{a}{1-x}-\frac{2}{2-x}+\frac{3}{3-x}-\frac{4}{4-x}+\frac{b}{5-x}=0
\]

be quadratic or reducible to a quadratic in \( x \)? Solve the equation for each case.

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