
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 $g\left( x \right)=\log_{a}\left( x-3 \right)+2$ ($a > 0,a\ne 1$), its graph passes through a fixed point $M$. If the graph of the power function $f\left( x \right)=x^{\alpha}$ also passes through point $M$, calculate the value of $\alpha$.

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