
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
There is a dry well, and you use a rope to measure the depth of the well. When the rope is folded in half and lowered to the bottom of the well, one end of the rope is $9 \text{ meters}$ above the well's mouth. When the rope is folded into thirds and lowered to the bottom of the well, one end of the rope is $2 \text{ meters}$ above the well's mouth. Find the length of the rope in meters and the depth of the well in meters.

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