
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
Under the action of the gravitational force $\dot{g}$, directed opposite to the $OZ$ axis, a unit mass body slides down a spiral:

$$
x=a \cos \varphi, \quad y=a \sin \varphi, \quad z=b(2 \pi-\varphi)
$$

from point $A(a, 0, 2 \pi b)$ to point $B(a, 0, 0)$.

Find the work done by the field during this movement.

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