
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 magical clock, in addition to the usual pair of hands, has a second pair that is symmetric to the first pair relative to the vertical axis. From a photograph of the clock, it is impossible to determine which hands are the real ones. Additionally, on magical clocks (like ordinary ones), it is impossible to distinguish morning from evening. Thus, several different times can correspond to the same photograph (for example, 1:15, 10:45, and 22:45 all look the same as shown on the right).

A robot takes several photographs of the clock over one day (from 0:00 to 24:00). It remembers the order in which the photographs were taken but not the exact time. Sometimes, from such a series of photographs, it is possible to determine the exact time of some of them; such photographs are called certain. If there are multiple possible times from the series of photographs for a specific image, it is called uncertain. For example, in the series of photographs shown on the right, photograph No. 2 is certain (it was taken at 9:00), whereas photograph No. 4 is uncertain (it could be taken at either 16:00 or 20:00).

Given a series of 100 photographs taken within one day, none of which look identical and none of which are taken at 0:00, 6:00, 12:00, 18:00, or 24:00, what is the minimum number of uncertain photographs among them?

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