
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
(1) Given the set $P=\{x|x^2+x-6=0\}$, and $S=\{x|ax+1=0\}$, with the condition that $S \subseteq P$, find the set consisting of all the possible values of the real number $a$.
(2) Given the set $A=\{x|-2\leq x\leq 5\}$, and $B=\{x|m+1\leq x\leq 2m-1\}$, with the condition that $B \subseteq A$, find the set consisting of all the possible values of the real number $m$.

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