
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
An $88$-key piano forms an increasing geometric sequence of frequencies from left to right. If the frequency of the middle $A$ (the $49$th key from the left) is $440$ Hz and the frequency of the lowest key on the piano is $27.5$ Hz, then the frequency of the $61$st key from the left is ____ Hz.

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