
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 three vectors in the plane: $$\overrightarrow {a} = (3, 2), \overrightarrow {b} = (-1, 2), \overrightarrow {c} = (4, 1)$$  
 (1) Find the coordinates of ($$\overrightarrow {a} + \lambda \overrightarrow {c}$$) and (2$$\overrightarrow {b} - \overrightarrow {a}$$)  
(2) If ($$\overrightarrow {a} + \lambda \overrightarrow {c}$$) is parallel to (2$$\overrightarrow {b} - \overrightarrow {a}$$), find the real number $\lambda$;  
(3) If ($$\overrightarrow {a} + \lambda \overrightarrow {c}$$) is perpendicular to (2$$\overrightarrow {b} - \overrightarrow {a}$$), find the real number $\lambda$.

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