
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 propositions $P: x^2 - 7x + 10 \leq 0$ and $Q: (x - 3)(x + 1) \leq 0$, find the range of real number $x$ that makes the proposition "$P$ and $Q$" true.

(2) Provide another proposition and discuss the relationship between its condition and conclusion from both the sufficiency and necessity perspectives.

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