
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
It is known that the graphs of the functions \( f(x)=x^{p} \) and \( g(x)=\ln x \) are tangent to each other (they have a common point where their tangents coincide). Find the constant \( p \) and the point of tangency. (16 points)

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