
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
Let $\alpha, \beta, \gamma \in \mathbf{R}$ satisfy the equation $\sin \alpha \cdot \cos \beta + |\cos \alpha \cdot \sin \beta| = \sin \alpha \cdot |\cos \alpha| + |\sin \beta| \cdot \cos \beta$. Then, find the minimum value of $(\tan \gamma - \sin \alpha)^2 + (\cot \gamma - \cos \beta)^2$.

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