
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 the function $f(x)=|x-4|+|x-a|$ $(a > 1)$, and the minimum value of $f(x)$ is $3$.
1. Find the value of $a$.
2. If $f(x)\leqslant 5$, find the set of all $x$ that satisfy the condition.

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