
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
The formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ remains $C = \frac{5}{9}(F-32)$. An integer Fahrenheit temperature is converted to Celsius, rounded to the nearest integer, then converted back to Fahrenheit using the formula $F' = \frac{9}{5}C' + 32$ where $C'$ is the rounded Celsius temperature, and $F'$ is finally rounded to the nearest integer. For how many integer Fahrenheit temperatures between 32 and 2000 inclusive does the original temperature equal the final temperature?

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