
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 that $f(x)$ is a function defined on the set of real numbers $\mathbb{R}$, and its inverse function is $f^{-1}(x)$. If $f^{-1}(x+a)$ and $f(x+a)$ are inverse functions of each other, and $f(a)=a$ (where $a$ is a non-zero constant), calculate the value of $f(2a)$.

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