
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 box, there are three cards labeled 1, 2, and 3. Two cards are drawn successively with replacement from this box, and the numbers on the drawn cards are denoted as $x$ and $y$, respectively. Let $O$ be the origin of coordinates, and point $B$ has coordinates $(x-2, x-y)$. Find the maximum value of $|\overrightarrow{OB}|$ and the probability that $|\overrightarrow{OB}|$ takes the maximum value.

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