
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 blue parabola in the coordinate plane has an equation of the form $x = ay^2 + by + c$. The vertex of the parabola is at point $(5,-3)$. The parabola also passes through the point $(7, 1)$. Determine the value of $c$ given these conditions.

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