
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
An isosceles trapezoid \(ABCD\) with bases \(BC\) and \(AD\) is given such that \(\angle ADC = 2 \angle CAD = 82^\circ\). Inside the trapezoid, a point \(T\) is chosen such that \(CT = CD\) and \(AT = TD\). Find \(\angle TCD\). Give your answer in degrees.

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