
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 batch of identical parts was processed on three different machines in the following sequence: first, only the first machine worked for as many hours as it would take for the second and third machines to jointly complete the entire job; then, only the second machine worked for as many hours as it would take for the first and third machines to jointly complete the entire job. The remaining parts in the batch were processed on the third machine for as many hours as it would take for the first and second machines to jointly complete the entire job.

By how many times faster would this work have been completed if all three machines had worked together?

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