
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 sequence $\{a\_n\}$, its reciprocal forms an arithmetic sequence in the original order, and a sequence $\{x\_n\}$ with all positive terms satisfies $x\_1=3$, $x\_1+x\_2+x\_3=39$, and $x\_n^{a\_n}= x\_{ n+1 }^{ a\_{n+1} }= x\_{ n+2 }^{ a\_{n+2 }}$, find $x\_n$.

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