
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
During this year's Science and Technology Festival, the school needs to award a total of $25$ winners from the "Smartest Brain" and "Comprehensive Ability Competition". It is required that the number of winners in the "Comprehensive Ability Competition" is not less than $5$ times the number of winners in the "Smartest Brain" competition.<br/>$(1)$ Find the maximum number of winners in the "Smartest Brain" competition.<br/>$(2)$ If the prize for the winners of the "Smartest Brain" competition is $15$ yuan each, and the prize for the winners of the "Comprehensive Ability Competition" is $30$ yuan each, then when the number of winners in the "Smartest Brain" competition is how many people, the total prize amount is the least?

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