
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 $\frac {x^{2}}{2}+y^{2}=1$ and the line $l: y=x+m$.  
(1) When the line $l$ intersects the ellipse, find the range of the real number $m$.  
(2) If the line $l$ passes through the right focus of the ellipse and intersects the ellipse at points A and B, find the length of chord AB.

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