
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 coordinates of the center of gravity of the arc $A B$ of the helical line $x=a \cos t, y=a \sin t, z=b t$, if at each point its linear density is proportional to the ordinate (z-coordinate) of that point; $t_{A}=0, t_{B}=\pi$.

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