
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
To encourage the physics interest group to carry out experimental projects, a certain school decided to purchase two sets of physics experiment kits, $A$ and $B$. The unit price of set $A$ is $1.2$ times the unit price of set $B$. The number of set $A$ purchased with $9900$ yuan is $5$ more than the number of set $B$ purchased with $7500$ yuan.  
$(1)$ Find the unit prices of sets $A$ and $B$.  
$(2)$ If the school is prepared to purchase a total of $20$ sets of physics experiment kits $A$ and $B$ for $3400$ yuan, how many sets of kit $B$ should be purchased at least?

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