
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
The equation  $166\times 56 = 8590$  is valid in some base  $b \ge 10$  (that is,  $1, 6, 5, 8, 9, 0$  are digits in base  $b$  in the above equation). Find the sum of all possible values of  $b \ge 10$  satisfying the equation.

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