
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
Define: For any number $a$, the symbol $\left[a\right]$ represents the largest integer not greater than $a$. For example, $\left[5.7\right]=5$, $\left[5\right]=5$, $\left[-1.5\right]=-2$. If $[\frac{4x-5}{5}]=-5$, all integers $x$ that satisfy the condition are ______.

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