
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 the system of linear inequalities in one variable $x$ is $\left\{\begin{array}{l}2({x+1})＜x+3\\ x-a≤a+5\end{array}\right.$ is $x \lt 1$, and $a$ is a non-positive integer, then determine the number of values of $a$ that satisfy the conditions.

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