
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 equations of the tangent and normal lines to the curve at the point corresponding to the parameter value $t=t_{0}$.

$\left\{\begin{array}{l}x=a(t-\sin t) \\ y=a(1-\cos t)\end{array}\right.$

$t_{0}=\frac{\pi}{3}$

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