
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 is shown on a coordinate grid where the equation of the parabola is \(y = ax^2 + bx + c\). Determine the value of \(c\). Assume the vertex of the parabola is at \((3, -5)\) and it passes through the point \((1, -3)\).

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