
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 given integer Fahrenheit temperature $F$ is first converted to Kelvin using the formula $K = \frac{5}{9}(F - 32) + 273.15$, rounded to the nearest integer, then converted back to Fahrenheit using the inverse formula $F' = \frac{9}{5}(K - 273.15) + 32$, and rounded to the nearest integer again. Find how many integer Fahrenheit temperatures between 100 and 500 inclusive result in the original temperature equaling the final temperature after these conversions and roundings.

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