
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
It is known that \(\frac{7}{13} + \sin \varphi = \cos \varphi\) for some real \(\varphi\). What is \(\sin 2 \varphi\)?

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