
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 signals are composed of the digits $0$ and $1$ with equal likelihood of transmission, the probabilities of error in transmission are $0.9$ and $0.1$ for signal $0$ being received as $1$ and $0$ respectively, and $0.95$ and $0.05$ for signal $1$ being received as $1$ and $0$ respectively.

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