
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 a sequence $\{a_n\}$, where $a_1=4$ and $a_{n+1}=a_n+2$ $(n\in \mathbb{N}^*)$,

$(1)$ Find the general formula for the sequence $\{a_n\}$;

$(2)$ Let $b_n=(\sqrt{2})^{a_n-2}-3n$, calculate the sum $|b_1|+|b_2|+|b_3|+\cdots+|b_{10}|$.

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