
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
A box contains five balls labeled $1$, $3$, $5$, $7$, and $9$. Two balls are drawn from the box simultaneously, with each ball having an equal chance of being selected.

(I) List all possible outcomes when two balls are drawn;
(II) Calculate the probability that the sum of the labels on the two drawn balls is divisible by $4$;
(III) If the smaller label is used as the $x$-coordinate and the larger label as the $y$-coordinate, determine the probability that the corresponding point lies on the line $y=x+2$.

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