
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) Write the converse, negation, and contrapositive of the proposition: "If $x^{2}-3x+2=0$, then $x=1$ or $x=2$," and determine their truth values;

(2) Given the sets $P=\{x\mid -1 < x < 3\}$ and $S=\{x\mid x^{2}+(a+1)x+a < 0\}$, and the necessary and sufficient condition for $x\in P$ is $x\in S$, find the value of the real number $a$.

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