
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 blue parabola shown is the graph of the equation $x = ay^2 + by + c$. Find $c$. Assume that the graph has a standard unit scale, and the vertex of this parabola is at $(5, 3)$. The parabola also passes through the point $(7, 1)$.

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