
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
Given an integer $a = 2k$ for some integer $k$, evaluate the outcomes of the following operations and determine which result in an even integer.
1. $a^2$ (squaring)
2. $2a$ (multiplication by two)
3. $a \mod 4$ (modulus operation with 4)
4. $\frac{a}{2}$ (division by two)
5. $a^3$ (cubing)

Determine the operations which always result in an even integer.
A) 1, 2, and 5
B) 1, 3, and 5
C) 1, 2, 3, and 5
D) 2, 3, and 4

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