
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 wholesaler purchased $50$ packs of shirts of size $L$ from a clothing manufacturer. Due to the negligence of the packaging workers, some packs were mixed with shirts of size $M$. The number of $M$ shirts mixed in (pieces) and the corresponding number of packs (packs) are shown in the table below:

|M shirts (pieces)|$0$|$1$|$4$|$5$|$7$|$9$|$10$|$11$|
|---|---|---|---|---|---|---|---|---|
|Packs| $7$| $3$| $10$| $15$| $5$| $4$| $3$| $3$|

A retailer randomly selected one pack from the $50$ packs. Find the probabilities of the following events:
$(1)$ No $M$ shirts were mixed in the pack;
$(2)$ $M$ shirts were mixed in the pack and the number of pieces is less than $7$;
$(3)$ The number of $M$ shirts mixed in the pack is more than $9$.

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