
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 graph of the quadratic \(y = ax^2 + bx + c\) has the following properties: 
1. The minimum value of \(y = ax^2 + bx + c\) is \(-5\), which occurs at \(x = 3\). 
2. The graph passes through the point \((0,5)\). 
If the graph also passes through the point \((5,m)\), then what is the value of \(m\)?

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