
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 that the angle of inclination of line $l$ is $θ$ and line $l$ is perpendicular to the line $x - 3y + 1 = 0$, find the value of $\frac{2}{3\sin^{2}{θ} - \cos^{2}{θ}}$.

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