
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 $f(x)=\ln x- \frac {x-a}{x}$, where $a$ is a constant, and $a > 0$.
(1) If the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is perpendicular to the line $y=x+1$, find the monotonically decreasing interval of the function $f(x)$;
(2) If the minimum value of the function $f(x)$ in the interval $[1,3]$ is $\frac {1}{3}$, find the value of $a$.

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