
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
Determine the value of \( c \) for which the expression

\[ (c-3)^{2}+(c-4)^{2}+(c-8)^{2} \]

is minimized. Will the value of \( |c-3|+|c-4|+|c-8| \) also be minimized for this \( c \)?

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