
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
In a certain measurement, it was found that a set of data $(x_i, y_i)$ has a strong correlation. It was calculated that $\hat{y} = x + 1$. However, for the data point $(1, y_0)$, $y_0$ is illegible but known to be any value in the interval $[0, 3]$. What is the probability that the absolute value of the residual for this data point is no more than 1? (Residual = actual value - predicted value)

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