
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
Suppose $p$ is a prime number. Determine which of the following expressions is guaranteed to be composite for every prime number $p$:
1. $p^2 + 17$
2. $p^2 + 35$
3. $p^2 + 39$
4. $p^2 + 41$
5. $p^2 + 105$
A) $p^2 + 17$
B) $p^2 + 35$
C) $p^2 + 39$
D) $p^2 + 41$
E) $p^2 + 105$

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