
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: $l_{1}$: $y=ax+3$ and $l_{2}$ symmetric about the line $y=x$, $l_{2}$ is parallel to $l_{3}$: $x+2y-1=0$, find the value of $a$.

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