
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
Given that \( a, b, c \) are all non-negative real numbers and \( a^{2}+b^{2}+c^{2}+ab+\frac{2}{3}ac+\frac{4}{3}bc=1 \), find the maximum and minimum values of \( a+b+c \).

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