
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
Calculate the arc length:
1) of the semicubical parabola $l^{2} = (x-1)^{3}$ between the points $A(2, -1)$ and $B(5, -8)$;
2) of one arch of the cycloid $x = a(t - \sin t)$, $y = a(1 - \cos t)$;
3) of the curve $\rho = a \cos^{3} \left(\frac{\varphi}{3}\right)$.

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