
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 event $A$ be "Point $M(x,y)$ satisfies $x^{2}+y^{2}\leqslant a(a > 0)$", and event $B$ be "Point $M(x,y)$ satisfies $\begin{cases} & x-y+1\geqslant 0 \\ & 5x-2y-4\leqslant 0 \\ & 2x+y+2\geqslant 0 \end{cases}$. If $P(B|A)=1$, then find the maximum value of the real number $a$.

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