
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
Xiao Qian, Xiao Lu, and Xiao Dai are guessing a natural number between 1 and 99. Here are their statements:

Xiao Qian says: "It is a perfect square, and it is less than 5."
Xiao Lu says: "It is less than 7, and it is a two-digit number."
Xiao Dai says: "The first part of Xiao Qian's statement is correct, but the second part is wrong."

If one of them tells the truth in both statements, one of them tells a lie in both statements, and one of them tells one truth and one lie, then what is the number? (Note: A perfect square is a number that can be expressed as the square of an integer, for example, 4=2 squared, 81=9 squared, so 4 and 9 are considered perfect squares.)

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