
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 a finite sequence {a<sub>n</sub>}, which satisfies the condition |a<sub>1</sub>-a<sub>2</sub>|≤|a<sub>1</sub>-a<sub>3</sub>|≤…≤|a<sub>1</sub>-a<sub>m</sub>|, it is said that {a<sub>n</sub>} has property P.  
(1) Determine whether the sequences 3, 2, 5, 1 and 4, 3, 2, 5, 1 have property P, and explain the reasons.  
(2) If a<sub>1</sub>=1, and the geometric sequence with a common ratio q, consisting of 10 terms, has property P, find the range of q.  
(3) If {a<sub>n</sub>} is a permutation of 1, 2, 3, ..., m (m≥4), and {b<sub>n</sub>} satisfies b<sub>k</sub>=a<sub>k+1</sub> (k=1, 2, ..., m-1), both {a<sub>n</sub>} and {b<sub>n</sub>} have property P, find all sequences {a<sub>n</sub>} that satisfy the conditions.

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