
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
Find the values of constants $a$ and $b$ such that when $3x + 4$ divides $3x^4 + ax^3 + bx^2 - 16x + 55$, the remainder is $23$, and when $x - 3$ divides it, the remainder is $10$.

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