
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
What is the maximum value that can be taken by the sum

$$
\left|x_{1}-1\right|+\left|x_{2}-2\right|+\ldots+\left|x_{63}-63\right|
$$

if $x_{1}, x_{2}, \ldots, x_{63}$ are some permutation of the numbers $1, 2, 3, \ldots, 63$?

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