
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 Celsius temperature \( C \) to the corresponding Fahrenheit temperature \( F \) is \( F = \frac{9}{5}C + 32 \). An integer Celsius temperature \( C \) is converted to Fahrenheit, rounded to the nearest tenth, converted back to Celsius, and rounded to the nearest integer. Determine for how many integer Celsius temperatures between -10 and 50 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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