
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 terminal side of angle $θ$ passes through the point $\left(2\sin^2 \frac{π}{8}-1,a\right)$, and $\sin θ=2 \sqrt{3}\sin \frac{13π}{12}\cos \frac{π}{12}$, find the real number $a$.

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