
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 Sarah walked one-third of the way from home to the library at a rate of $w$ meters per minute, where the total distance to the library is $d$ meters, and she jogged the remaining $\frac{2}{3}d$ at a rate of $4w$ meters per minute, given that she took 9 minutes to walk the first one-third of the way to the library, calculate the total time it took Sarah to get from home to the library.

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