
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
If $g(x) = x^2 + 3x + 1$ for all real $x$, find the largest value of $c$ such that:
"$|g(x) - 1| \leq c$ whenever $|x - 1| \leq d$ and $c > 0$ and $d > 0$."
A) $c = 3$
B) $c = 4$
C) $c = 5$
D) $c = 6$

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