
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
Find the continuous function  $ f(x)$  such that  $ xf(x)\minus{}\int_0^x f(t)\ dt\equal{}x\plus{}\ln (\sqrt{x^2\plus{}1}\minus{}x)$  with  $ f(0)\equal{}\ln 2$ .

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