
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 maximum value of \( y = ax^2 + bx + c \) is 7, which occurs at \( x = 2 \).
2. The graph passes through the point \( (0, -7) \).
If the graph passes through the point \( (5, n) \), then what is the value of \( n \)?

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