
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
Given the function f(x) = ax^2 + 2x + c (a, c ∈ ℕ*), satisfy the following conditions:
1. f(1) = 5
2. 6 < f(2) < 11
(1) Find the values of a and c.
(2) Let g(x) = f(x) - 2x - 3 + |x - 1|, find the minimum value of g(x).

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