
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 that the sequence $\{x_{n}\}$ has $4$ terms with $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$ being a selection from $\{1,2,3,4,5\}$, and $\{x_{n}\}$ is a "locally arithmetic" sequence, calculate the conditional probability of being a "locally arithmetic" sequence given the selection of its terms.

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