
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
(The full score for this question is 10 points.) Given that the parabola $f(x) = ax^2 + bx - 7$ passes through the point $(1,1)$, and the equation of the tangent line at this point is $4x - y - 3 = 0$, find the values of $a$ and $b$.

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