
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
Consider a guessing game involving a two-digit number. Here are the clues given to guess the number:
1. It is a two-digit integer.
2. The tens digit is odd.
3. Both digits add up to an even number.
4. The number is between 40 and 80.
What is the probability that a guess following these clues will be the correct number? Express your answer as a common fraction.

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