
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
In a given plane, four lines $m, n, p,$ and $q$ are parallel. Line $t$ intersects these lines at points $A, B, C$, and $D$ respectively. Angles at intersections are given as follows: $\angle BAT = 50^\circ$, $\angle DBT = 140^\circ$. Determine the measure of $\angle BCT$.

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