
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
(1) For what value of $a$ are the lines $l_{1}: y=-x+2a$ and $l_{2}: y=(a^{2}-2)x+2$ parallel?  
(2) For what value of $a$ are the lines $l_{1}: y=(2a-1)x+3$ and $l_{2}: y=4x-3$ perpendicular?

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