
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 \\(f(x)\\) be an even function, and it is a monotonic function when \\(x > 0\\). Find the sum of all \\(x\\) that satisfy \\(f(2x) = f\left(\dfrac{x+1}{x+4}\right)\\).

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