
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
The development of our country's measurement system has a long history. In the Warring States period, there appeared "ring weights" similar to weights used to measure the mass of objects. It is known that the masses (unit: zhu) of 9 ring weights form a sequence $\{a_{n}\}$ with 9 terms from small to large. The first 3 terms of this sequence form an arithmetic sequence, and the last 7 terms form a geometric sequence. Given that $a_{1}=1$, $a_{5}=12$, and $a_{9}=192$, find $a_{7}=$______ and the sum of all terms in the sequence $\{a_{n}\}=$______.

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