
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
For any non-zero real numbers $a$ and $b$, if $a \otimes b = \begin{cases} \frac{b-1}{a}, a < b \\ \frac{a+1}{b}, a\geqslant b \end{cases}$, then $\lg 10000\otimes \left( \frac{1}{2}\right) ^{-2}=$_______.

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