
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 \( f(x) = x^3 + 2x^2 + 3x + 4 \) and let \( T \) be the set of integers \( \{0, 1, 2, \dots , 50 \} \). Find the number of members \( t \) of \( T \) such that \( f(t) \) leaves a remainder of zero when divided by \( 8 \).

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