
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
A Martian traffic light consists of six identical bulbs arranged in two horizontal rows (one below the other) with three bulbs in each row. A rover driver in foggy conditions can distinguish the number and relative positions of the lit bulbs on the traffic light (for example, if two bulbs are lit, whether they are in the same horizontal row or different ones, whether they are in the same vertical column, adjacent vertical columns, or in the two outermost vertical columns). However, the driver cannot distinguish unlit bulbs and the traffic light's frame. Therefore, if only one bulb is lit, it is impossible to determine which of the six bulbs it is. How many different signals from the Martian traffic light can the rover driver distinguish in the fog? If none of the bulbs are lit, the driver cannot see the traffic light.

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