
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
Consider the functions $f(x) = e^x+\sin x$ and $g(x) = x - 2$. Let $P(x_1, f(x_1))$ and $Q(x_2, g(x_2))$ ($x_1 \geq 0, x_2 > 0$). If the line $PQ$ is parallel to the x-axis, calculate the shortest distance between points $P$ and $Q$.

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