
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 the function $f(x)=\log_{a}(x-2)+4$ ($a > 0$ and $a \neq 1$), its graph passes through a fixed point $P$. The initial side of angle $\alpha$ coincides with the positive half-axis of the $x$-axis, the vertex coincides with the origin, and the terminal side passes through point $P$. Then, $\frac{\sin \alpha + 2\cos \alpha}{\sin \alpha - \cos \alpha}=$ \_\_\_\_\_\_.

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