
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
In $\triangle ABC$, the sides corresponding to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Let condition $p$ be $a \leqslant \frac{b+c}{2}$, and condition $q$ be $A \leqslant \frac{B+C}{2}$. Determine the relationship between condition $p$ and condition $q$.

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