
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 an ellipse with its center at the origin, foci on the x-axis, and an eccentricity of $$\frac{\sqrt{3}}{2}$$, a line l passes through point M(-1, 0) and intersects the ellipse at points P and Q.
(1) If the slope of line l is 1 and $$\overrightarrow{PM} = -\frac{3}{5}\overrightarrow{QM}$$, find the standard equation of the ellipse.
(2) If the right vertex of the ellipse in part (1) is A and the inclination angle of line l is α, find the value of α when $$\overrightarrow{AP} \cdot \overrightarrow{AQ}$$ reaches its maximum, and compute this maximum value.

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