
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
It is known that the sequence ${a_n}$, when inverted in sequence, forms an arithmetic sequence, and another 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 the general term of the sequence ${x_n}$.

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