
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 $f(x)= \dfrac {2}{1+2^{x}}+ \dfrac {1}{1+4^{x}}$ that satisfies the condition $f(\log _{a}( \sqrt {2}+1))=1$, where $a > 1$, find the value of $f(\log _{a}( \sqrt {2}-1))$.

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