
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
From the same deck of cards with identical backs, $9$ hearts, $10$ spades, and $11$ diamonds are drawn.<br/>$(1)$ After shuffling the drawn cards with the backs facing up on the table, find the probability of randomly drawing a heart from them;<br/>$(2)$ If $9$ hearts and $m\left(m \gt 6\right)$ spades are first removed from the drawn cards, and the remaining cards are shuffled with the backs facing up on the table, then a card is randomly drawn from the table.<br/>① For what value of $m$ is the event "the card drawn next is a diamond" a certain event?<br/>② For what value of $m$ is the event "the card drawn next is a diamond" a random event? Also, find the minimum value of the probability of this event.

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