
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 there are $5$ balls of the same size and texture in an opaque bag, including $3$ black balls (denoted as $B_{1}$, $B_{2}$, and $B_{3}$) and $2$ red balls (denoted as $R_{1}$ and $R_{2}$). <br/> $(1)$ Find the probability of randomly drawing a red ball; <br/> $(2)$ If two balls are drawn without replacement, find the probability that both balls are black.

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