
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
If  $x$  is a real number satisfying the equation   $$ 9\log_3 x - 10\log_9 x =18 \log_{27} 45, $$   then the value of  $x$  is equal to  $m\sqrt{n}$ , where  $m$  and  $n$  are positive integers, and  $n$  is not divisible by the square of any prime. Find  $m+n$ .

*Proposed by pog*

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