
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 $γ$ and $θ$ are constants, where $θ ∈ (0, \frac{π}{4})$ and $γ ∈ (\frac{π}{4}, \frac{π}{2})$, if the equation $\sin(α + γ) + \sin(γ - β) = \sin θ (\sin α - \sin β) + \cos θ (\cos α + \cos β)$ holds true for all $α, β ∈ R$, calculate the value of $\frac{\tan θ \tan γ + \cos (θ - γ)}{\sin^2(θ + \frac{π}{4})}$.

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