
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
Find the maximum value of the expression

$$
\frac{a}{x} + \frac{a+b}{x+y} + \frac{a+b+c}{x+y+z}
$$

where \( a, b, c \in [2,3] \), and the triplet of numbers \( x, y, z \) is some permutation of the triplet \( a, b, c \).

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