
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
Dobrákovi planted tulips in a square garden with a side length of 6 meters. Later, they built a square terrace with a side length of 7 meters attached to their house. One vertex of the terrace was located exactly in the middle of the tulip garden, and one side of the terrace divided one side of the tulip garden in the ratio \(1:5\).

In what ratio did the other side of the terrace divide the other side of the garden? By how many square meters did the tulip garden decrease due to the construction of the terrace?

(L. Hozová)

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