
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 number, 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 half of Xiao Qian’s statement is true, but the second half is false."

If among these 3 people, one person’s two statements are both true, one person’s two statements are both false, and one person’s one statement is true and the other is false, then what is the number? (Note: A perfect square number is a number that can be expressed as the square of an integer, for example, $4=2^2$, $81=9^2$, so we call 4, 9 perfect square numbers).

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