
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 smallest real number $c$ such that \[|x_1| + |x_2| + \dots + |x_9| \geq c|M|\] whenever $x_1, x_2, \ldots, x_9$ are real numbers such that $x_1+x_2+\cdots+x_9 = 10$ and $M$ is the median of $x_1, x_2, \ldots, x_9$.

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