
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 four numbers $1$, $x\_1$, $x\_2$, $2$ that form an arithmetic sequence, and four numbers $1$, $y\_1$, $y\_2$, $2$ that form a geometric sequence. Consider points $P\_1(x\_1, y\_1)$ and $P\_2(x\_2, y\_2)$. Determine the relationship between these points and the line $y=x$.

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