
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 $A(0, 2)$, point $P$ lies on the line $x + y + 2 = 0$, and point $Q$ lies on the circle $x^2 + y^2 - 4x - 2y = 0$. Find the minimal value of $|PA| + |PQ|$.

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