
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
 $p,q$  satisfies  $px+q\geq \ln x$  at  $a\leq x\leq b\ (0<a<b)$ .

Find the value of  $p,q$  for which the following definite integral is minimized and then the minimum value.

\[\int_a^b (px+q-\ln x)dx\]

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