
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 \(g(x) = x^2 + 5x + 4\), and let \(T\) be the set of integers \(\{0, 1, 2, \ldots, 30\}\). Determine the number of members \(t\) of \(T\) such that \(g(t)\) has remainder zero when divided by \(10\).

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