
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 $max\{a,b\}=\left\{\begin{array}{l}a,a≥b\\ b,a＜b\end{array}\right.$, if the sum of the first $n$ terms of the sequence $\{a_{n}\}$ is $S_{n}$, $a_{6}=16$, and $a_{n+1}=\max \{a_{n}+3$,$2a_{n}\}$, then $S_{7}=\_\_\_\_\_\_$.

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