
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
How many integer Fahrenheit temperatures between 50 and 500 inclusive, when converted to Celsius using the formula $C = \frac{5}{9}(F-32)$, rounded down (instead of the nearest integer), returned back to Fahrenheit using $F' = \left \lfloor \frac{9}{5}C \right\rfloor + 32$, and rounded down, yield the same original Fahrenheit temperature?

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