
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 $f(x)= \begin{cases} (\frac{1}{2})^{x-1}\;,\;x\leqslant 1 \\\\ \log_{3}(x+1)\;,\;x > 1\\end{cases}$, find the solution set of the inequality $f(x+1)-1 > 0$.

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