
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
If the solution set of inequality (group) ① satisfies inequality (group) ②, then inequality (group) ① is said to be covered by inequality (group) ②. In particular, if an inequality (group) has no solution, it is covered by any other inequality (group). For example, the inequality $x \gt 2$ is covered by the inequality $x \gt 1$, and the inequality group $\left\{\begin{array}{l}{x＜3}\\{x≥5}\end{array}\right.$ has no solution, so it is covered by any other inequality (group). If the inequality group about $x$ is $\left\{\begin{array}{l}{2a-x＞1}\\{2x+5＞3a}\end{array}\right.$, and it is covered by $1\leqslant x\leqslant 6$, then the range of $a$ is ______.

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