
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
Let $a, b, c$ be integers such that $1 \le a \le b \le c \le 5.$ Find the minimum value of
\[(a - 2)^2 + \left(\frac{b+1}{a} - 1\right)^2 + \left(\frac{c+1}{b} - 1\right)^2 + \left(\frac{5}{c} - 1\right)^2.\]

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