
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 cake is divided into three parts. If two-thirds of the first part are cut off and added to the second part, then the third part becomes twice as large as the first part but half as large as the second part. What fraction of the cake do the cut-off pieces constitute?

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