
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
A green parabola is indicated on the graph of the equation $x = ay^2 + by + c$. Find $a + b + c$.
The vertex of the parabola is at $(7, -6)$, and it is known to pass through the point $(1, 0)$.

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