
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 $f(x)=|x-a|$,  
(1) If the solution set of the inequality $f(x) \leqslant 3$ is $\{x|-1 \leqslant x \leqslant 5\}$, find the value of the real number $a$;  
(2) Under the condition of (1), if there exists a real number $x$ such that the inequality $f(x)+f(x+5) < m$ holds, find the range of values for the real number $m$.

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