
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
Darren has borrowed $200$ clams from Ethan at an initial $8\%$ simple daily interest, and after 10 days, the interest rate drops to $6\%$. Fergie has borrowed $300$ clams from Gertie at a $4\%$ simple daily interest. Determine how many days will pass until Darren and Fergie owe the same amount, assuming no repayments are made during this time.

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