
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 stone is thrown into a well and it takes a total of \( 10 \) seconds for the stone to hit the bottom and the sound of the impact to travel back up. If the stone falls according to the law \( d = 20t_1^2 \) feet in \( t_1 \) seconds and the velocity of sound is unchanged at \( 1120 \) feet per second, find the new depth of the well.

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