
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
The work ratios of projects A, B, and C are $1: 2: 3$. They are undertaken by three teams, Team 1, Team 2, and Team 3, respectively, all starting at the same time. After a certain number of days, the amount of work completed by Team 1 is half of the amount of work not completed by Team 2, the amount of work completed by Team 2 is one-third of the amount of work not completed by Team 3, and the amount of work completed by Team 3 equals the amount of work not completed by Team 1. What is the ratio of the work efficiencies of Teams 1, 2, and 3?

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