
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]


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It is known that for three consecutive natural values of the argument, the quadratic function \( f(x) \) takes the values 6, 5, and 5, respectively. Find the minimum possible value of \( f(x) \).

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