
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
Laura is training for a triathlon and decides to include all three components in her workout. She swims $2$ miles at a speed of $y$ miles per hour, then takes a 10-minute break. After that, she bikes $30$ miles at $3x + 2$ miles per hour, takes another 10-minute break to change to her running shoes, and finally runs $8$ miles at $x$ miles per hour. Her total workout, including all activities and breaks, lasts $200$ minutes. Determine how fast Laura ran and swam, to the nearest hundredth of a mile per hour.

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