
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 the function f(x) = a\*ln(x), where a belongs to the set of real numbers, and the function g(x) = $$\sqrt {x}$$, if these two functions share a common tangent line at their intersection point, find the value of the real number a.

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