
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
Given the function \( y=x^2+bx+c \) (where \( b \) and \( c \) are constants) passes through the point (-2,4).  
(1) Find the relationship between \( b \) and \( c \).  
(2) Let the coordinates of the vertex of the function graph be (m,n). When the value of \( b \) changes, find the analytical expression of \( n \) in terms of \( m \).

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