
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 certain distributor sells two types of mascots, large and small. The price of a large mascot is $1.5$ times the price of a small mascot. The number of small mascots purchased with $1200$ yuan is $5$ more than the number of large mascots purchased.  
$(1)$ Find the prices of the small and large mascots.  
$(2)$ In January, the distributor sold $500$ small mascots and $300$ large mascots. In February, the distributor decided to reduce the prices of both types of mascots by $a$ yuan. It is known that the number of small mascots sold in February is $10a$ more than in January, and the number of large mascots sold remains the same as in January. The total sales revenue for the distributor in February was $75000$ yuan. Find the value of $a$.

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