
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
Given $$\overrightarrow{a} = (2, 1)$$, $$\overrightarrow{b} = (1, -3)$$, if $$\overrightarrow{c} = \overrightarrow{a} + 2\overrightarrow{b}$$, $$\overrightarrow{d} = 2\overrightarrow{a} - x\overrightarrow{b}$$, and $$\overrightarrow{c}$$ is perpendicular to $$\overrightarrow{d}$$, then find the value of x.

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