
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
Let $g(x) = x^2 + 5x + 3$ and let $T$ be the set of integers $\{0, 1, 2, \dots , 30\}$. Find the number of members $t$ of $T$ such that $g(t)$ has remainder zero when divided by $10$.
A) 0
B) 1
C) 2
D) 3
E) 4

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