
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 $f(x)=\begin{cases} 
\log_{2}(x+1), & x > 3, \\
2^{x-3}+1, & x\leqslant 3, \\
\end{cases}$, and $f(a)=3$, calculate the value of $f(a-5)$.

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