
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
$$
f(x) = 3ax^2 - 2bx + c,
$$

where \( a - b + c = 0 \), \( f(0) > 0 \), and \( f(1) > 0 \), find the range of values for \( \frac{a + 3b + 7c}{2a + b} \).

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