
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
 $x$  is a base- $10$  number such that when the digits of  $x$  are interpreted as a base- $20$  number, the resulting number is twice the value as when they are interpreted as a base- $13$  number. Find the sum of all possible values of  $x$ .

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