
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 ellipse $x^2+4y^2=4$, and the line $l: y=x+m$  
(1) If $l$ intersects the ellipse at one point, find the value of $m$;  
(2) If $l$ intersects the ellipse at points $P$ and $Q$, and $|PQ|$ is equal to the length of the short axis of the ellipse, find the value of $m$.

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