
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 $$C: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ with a focal length of $$4 \sqrt {2}$$ and a minor axis length of 2. A line $l$ passing through point P(-2, 1) with a slope of 1 intersects the ellipse $C$ at points $A$ and $B$.  
(1) Find the standard equation of the ellipse $C$;  
(2) Find the length of chord $AB$.

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