
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 solution set of the inequality $x^{2}+bx+c > 0$ is $\{x | x > 2\}$ or $x < 1\}$,  
(1) Find the values of $b$ and $c$;  
(2) Find the solution set for the inequality $cx^{2}+bx+1 \leqslant 0$.

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