
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
Analyze the function $y=x^2 - 4x + 6$ by:
(1) Identifying the direction that the graph opens, the equation of the axis of symmetry, and the coordinates of the vertex;
(2) Describing how the graph can be obtained by translating the graph of $y=x^2$;  
(3) Finding the maximum or minimum value of the function.

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