
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 manufacturer initially has a machine that can address $600$ envelopes in $10$ minutes. He has now added two more machines. The first added machine can handle the same amount of envelopes in $5$ minutes, and together, the two machines can address $600$ envelopes in $3$ minutes. He intends all three machines to address $600$ envelopes in $1$ minute. What time should the second added machine alone take to address $600$ envelopes such that all three machines working together achieve this?
**A)** $\frac{10}{7}$ minutes
**B)** $\frac{12}{7}$ minutes 
**C)** $\frac{15}{7}$ minutes 
**D)** $\frac{8}{7}$ minutes

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