
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
Given that Alice has a collection of $30$ coins, consisting of $5$-cent coins, $10$-cent coins, and $25$-cent coins, and she has $4$ more $10$-cent coins than $5$-cent coins, and the total value of her collection is $410$ cents, determine how many more $25$-cent coins Alice has than $5$-cent coins.

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