
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
Determine which of the following operations always map even integers to even integers:
1. Squaring an even integer.
2. Taking the square root of a perfect square even integer.
3. Multiplying an even integer by an odd integer.
4. Raising an even integer to the power of 3.
5. Adding an odd integer to an even integer.
A) 1, 2, 3
B) 1, 2, 3, 4
C) 1, 3, 4
D) 3, 4, 5

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