
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
Find the possible dimensions $x$ and $y$ of the new rectangle $T$, where $y < 10$ cm, such that the perimeter of $T$ is one-half that of rectangle $S$ with dimensions $10$ cm and $15$ cm, and the area of $T$ is one-fourth that of $S$.

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