
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
Let \( x > 0 \), plane vectors \( \overrightarrow{A B} = (0,1), \overrightarrow{B C} = (1,2) \), and \( \overrightarrow{C D} = \left(\log_{3} x, \log_{9} x\right) \). If \( \overrightarrow{A C} \cdot \overrightarrow{B D} = 2 \), then find the value of \( x \).

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