
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
Let $\{a_n\}$ be an arithmetic sequence, and $\{b_n\}$ be a geometric sequence with all positive terms, and $a_1=2$, $b_1=3$, $a_3+b_5=56$, $a_5+b_3=26$.

(1) Find the explicit formula for the sequences $\{a_n\}$ and $\{b_n\}$.

(2) If the inequality $-x^2+3x\leqslant \frac{2b_n}{2n+1}$ is always true for any positive integer $n$, find the range of the real number $x$.

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