
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
Solve the following equations:

$$
\begin{aligned}
& \text{a)} \frac{1}{x-1}+\frac{3}{x-3}-\frac{9}{x-5}+\frac{5}{x-7}=0 \\
& \text{b)} \frac{3}{x+1}+\frac{5}{x-1}-\frac{3}{x-3}-\frac{5}{x-5}=0 \\
& \text{c)} \frac{19}{x+3}+\frac{21}{x+1}-\frac{27}{x-1}+\frac{35}{x-3}=0 \\
& \text{d)} \frac{3}{x-3}-\frac{1}{x-2}-\frac{1}{x+1}+\frac{3}{x+2}=0
\end{aligned}
$$

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