
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 $y=\log _{a}(x-1)+4(a \gt 0$ and $a\neq 1)$, whose graph always passes through a fixed point $P$, and point $P$ lies on the graph of the power function $y=f\left(x\right)$, find $\lg f\left(2\right)+\lg f\left(5\right)$.

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