
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 $a > 0$ and $a \neq 1$, $b > 0$ and $b \neq 1$, if for any values of $a$ and $b$ within the given range, the function $y=x+\log_{a}(x-2)$ and the function $y=b^{x-c}+2$ always pass through the same fixed point, then the real number $c=$ ______.

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