
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 two lines $l_{1}$ passing through points $A(3,a)$, $B(a-1,2)$, and $l_{2}$ passing through points $C(1,2)$, $D(-2,a+2)$, find the value of $a$ under the following conditions: $(1) l_{1} \parallel l_{2}; (2) l_{1} \perp l_{2}$.

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