
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 the function $f(x)$ be defined on $\mathbb{R}$ and satisfy for all $x, t \in \mathbb{R}$, and $t \neq 0$, we have $t(f(x+t)-f(x)) > 0$. Then, the number of elements in $\{(x, y) | y = f(x)\} \cap \{(x, y) | y = a\}$ is ____.

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