
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
Given that a box contains a total of 400 tickets in five colours: blue, green, red, yellow, and orange, where the ratio of blue to green to red tickets is $1: 2: 4$ and the ratio of green to yellow to orange tickets is $1: 3: 6$, find the smallest number of tickets that must be drawn to ensure that at least 50 tickets of one colour have been selected.

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