
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 a parabola symmetric about the y-axis, its vertex is at the origin, and it passes through point M ($$\sqrt{3}, -2\sqrt{3}$$).

(1) Find the standard equation of the parabola.  
(2) If the line $$y = x + m$$ intersects this parabola at two distinct points, find the range of values for $$m$$.

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