
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 \( C \) is \( C = \frac{5}{9}(F-32) \). Then, convert back to Fahrenheit using a modified formula \( F' = \frac{9}{5}C + 33 \) (instead of \( +32 \)). Assume each temperature is rounded to the nearest integer during each conversion.
For how many integer Fahrenheit temperatures between 34 and 1024 inclusive does the original temperature equal the final temperature after these conversions?

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