
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 $a+b+c=1$,  
(1) Find the minimum value of $S=2a^2+3b^2+c^2$ and the values of $a$, $b$, $c$ when $S$ is minimized.  
(2) If $2a^2+3b^2+c^2=1$, find the range of values for $c$.

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