
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
The sum of three numbers $a, b$, and $c$ is 84. If we decrease $a$ by 5, we get the value $T$. If we increase $b$ by 9, we also get the value $T$. If we multiply $c$ by 5, we also get the value $T$. What is the value of $T$?

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