
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 quadratic function $y=2x^{2}+4x-6$.  
$(1)$ Express the analytical expression of the quadratic function in the form of $y=a\left(x-h\right)^{2}+k$.  
$(2)$ The axis of symmetry of the graph of the quadratic function $y=2x^{2}+4x-6$ is the line ______, and the coordinates of the vertex are ______.

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