
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 set of positive real numbers  $x$  that satisfy  $2 | x^2 - 9 | \le 9 | x | $  is an interval  $[m, M]$ . Find  $10m + M$ .

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